## Futures price and expected future spot price

ankuragrawal.nit
Finance Junkie
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Joined: Sun Apr 01, 2012 10:52 am

### Futures price and expected future spot price

Futures price is an unbiased estimator of futures spot price in absence of systematic risk.
When the return from asset is positively corre;ated with mkt positive systematic risk, hence more compensation reqd by investor than Rf(risk free rate)
consider a future on stock indices...
positive correlation with the underlying hence positive systematic risk
Let q be the return calc as a percentage of income as dividends...
then investor in stock index ould require more than (Rf-q) compensation for bearing postive systematic risk...
This would mean that futures price in case of a stock index understates the expected spot price because of the formula F0=S0*exp(r-q)T..So my futures price would always go up hence this argument shows that I should always benefit in a stock index if I hold a long position hich obviously cannot be true,else everybody will make profit by holding a long posn in futures on index...
What am I missing?
Thnx...
Do let me know if my question is not absolutely clear...

Also how is futures price below CMP= Normal backwardation?
We know that futures price below "Expected spot price" is Normal Backwardation...

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ankuragrawal.nit
Finance Junkie
Posts: 64
Joined: Sun Apr 01, 2012 10:52 am

### Re: Futures price and expected future spot price

I know that the formula gives the non arbitrage price...So If I calculate F0 using this formula it will always understate the F0 which is there in the ticker in real world market because that F0 has systematic risk compensation included right?

Can you be more elaborate on the first paragraph by giving me an example from real life...
Say Nifty fut (march delivery) is trading at 5660.20 today...I go long in a Nifty future for march call because I believe feb future won't be good as clearance will be on last thursday i.e. 24/02
so my F0( given by ticker)=5660.20 right?
today's S0= 5607...If I calculate F0 using the risk free rate that SBI gives me F0 will be different from the F0 that is given by the ticker.

If no market risk was present then Nifty will rise to "F0 calculated by me using the Rf given by SBI on a principal of 5607" from 5607( today's close i.e. 21/02), right?
but since market risk is present so F0 is 5660.20
Am I getting all the concepts correctly here...Do tell me If my question is not clear...because this is confusing me...I need to understand what I am learning else FRM becomes just another certificate exam..Hence my questions might seem a bit silly but they serve as a way of giving a solid base to me before I take off...
Thank you!

ankuragrawal.nit
Finance Junkie
Posts: 64
Joined: Sun Apr 01, 2012 10:52 am

### Re: Futures price and expected future spot price

Can you plz tell me which part of the question is not clear or the whole question is not clear. Basically I wanted to ask if we can use these formulas F0=S0*....
in real world stock markets...and If yes then how as in do arbitrageurs really use these type of formulas to determine arbitrage opportunities in real world markets...Suppose I trade in Nifty futures daily..Is this formula of help to me somehow?

T-Bill rate is used a s risk free rate for all the countries? ( I thought only US uses T-Bill or is it that India has its own T-Bills ?)

ankuragrawal.nit
Finance Junkie
Posts: 64
Joined: Sun Apr 01, 2012 10:52 am

Thank you